TSTP Solution File: SET592+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:13:46 EDT 2022
% Result : Theorem 1.76s 1.93s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 10 RR)
% Number of literals : 13 ( 5 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,empty_set)
| A = empty_set ),
file('SET592+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ subset(A,B)
| ~ subset(A,C)
| subset(A,intersection(B,C)) ),
file('SET592+3.p',unknown),
[] ).
cnf(16,axiom,
dollar_c3 != empty_set,
file('SET592+3.p',unknown),
[] ).
cnf(17,plain,
empty_set != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
[iquote('copy,16,flip.1')] ).
cnf(28,axiom,
subset(dollar_c3,dollar_c2),
file('SET592+3.p',unknown),
[] ).
cnf(29,axiom,
subset(dollar_c3,dollar_c1),
file('SET592+3.p',unknown),
[] ).
cnf(31,axiom,
intersection(dollar_c2,dollar_c1) = empty_set,
file('SET592+3.p',unknown),
[] ).
cnf(43,plain,
subset(dollar_c3,empty_set),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[29,2,28]),31]),
[iquote('hyper,29,2,28,demod,31')] ).
cnf(59,plain,
empty_set = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[43,1])]),
[iquote('hyper,43,1,flip.1')] ).
cnf(61,plain,
$false,
inference(binary,[status(thm)],[59,17]),
[iquote('binary,59.1,17.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:46:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.76/1.93 ----- Otter 3.3f, August 2004 -----
% 1.76/1.93 The process was started by sandbox on n028.cluster.edu,
% 1.76/1.93 Wed Jul 27 10:46:49 2022
% 1.76/1.93 The command was "./otter". The process ID is 4623.
% 1.76/1.93
% 1.76/1.93 set(prolog_style_variables).
% 1.76/1.93 set(auto).
% 1.76/1.93 dependent: set(auto1).
% 1.76/1.93 dependent: set(process_input).
% 1.76/1.93 dependent: clear(print_kept).
% 1.76/1.93 dependent: clear(print_new_demod).
% 1.76/1.93 dependent: clear(print_back_demod).
% 1.76/1.93 dependent: clear(print_back_sub).
% 1.76/1.93 dependent: set(control_memory).
% 1.76/1.93 dependent: assign(max_mem, 12000).
% 1.76/1.93 dependent: assign(pick_given_ratio, 4).
% 1.76/1.93 dependent: assign(stats_level, 1).
% 1.76/1.93 dependent: assign(max_seconds, 10800).
% 1.76/1.93 clear(print_given).
% 1.76/1.93
% 1.76/1.93 formula_list(usable).
% 1.76/1.93 all A (A=A).
% 1.76/1.93 all B (subset(B,empty_set)->B=empty_set).
% 1.76/1.93 all B C D (subset(B,C)&subset(B,D)->subset(B,intersection(C,D))).
% 1.76/1.93 all B (-member(B,empty_set)).
% 1.76/1.93 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.76/1.93 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.76/1.93 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.76/1.93 all B C (intersection(B,C)=intersection(C,B)).
% 1.76/1.93 all B subset(B,B).
% 1.76/1.93 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.76/1.93 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.76/1.93 -(all B C D (subset(B,C)&subset(B,D)&intersection(C,D)=empty_set->B=empty_set)).
% 1.76/1.93 end_of_list.
% 1.76/1.93
% 1.76/1.93 -------> usable clausifies to:
% 1.76/1.93
% 1.76/1.93 list(usable).
% 1.76/1.93 0 [] A=A.
% 1.76/1.93 0 [] -subset(B,empty_set)|B=empty_set.
% 1.76/1.93 0 [] -subset(B,C)| -subset(B,D)|subset(B,intersection(C,D)).
% 1.76/1.93 0 [] -member(B,empty_set).
% 1.76/1.93 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.76/1.93 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.76/1.93 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.76/1.93 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.76/1.93 0 [] subset(B,C)|member($f1(B,C),B).
% 1.76/1.93 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.76/1.93 0 [] B!=C|subset(B,C).
% 1.76/1.93 0 [] B!=C|subset(C,B).
% 1.76/1.93 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.76/1.93 0 [] intersection(B,C)=intersection(C,B).
% 1.76/1.93 0 [] subset(B,B).
% 1.76/1.93 0 [] -empty(B)| -member(C,B).
% 1.76/1.93 0 [] empty(B)|member($f2(B),B).
% 1.76/1.93 0 [] B!=C| -member(D,B)|member(D,C).
% 1.76/1.93 0 [] B!=C|member(D,B)| -member(D,C).
% 1.76/1.93 0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 1.76/1.93 0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 1.76/1.93 0 [] subset($c3,$c2).
% 1.76/1.93 0 [] subset($c3,$c1).
% 1.76/1.93 0 [] intersection($c2,$c1)=empty_set.
% 1.76/1.93 0 [] $c3!=empty_set.
% 1.76/1.93 end_of_list.
% 1.76/1.93
% 1.76/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.76/1.93
% 1.76/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.76/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.93 deletion, with positive clauses in sos and nonpositive
% 1.76/1.93 clauses in usable.
% 1.76/1.93
% 1.76/1.93 dependent: set(knuth_bendix).
% 1.76/1.93 dependent: set(anl_eq).
% 1.76/1.93 dependent: set(para_from).
% 1.76/1.93 dependent: set(para_into).
% 1.76/1.93 dependent: clear(para_from_right).
% 1.76/1.93 dependent: clear(para_into_right).
% 1.76/1.93 dependent: set(para_from_vars).
% 1.76/1.93 dependent: set(eq_units_both_ways).
% 1.76/1.93 dependent: set(dynamic_demod_all).
% 1.76/1.93 dependent: set(dynamic_demod).
% 1.76/1.93 dependent: set(order_eq).
% 1.76/1.93 dependent: set(back_demod).
% 1.76/1.93 dependent: set(lrpo).
% 1.76/1.93 dependent: set(hyper_res).
% 1.76/1.93 dependent: set(unit_deletion).
% 1.76/1.93 dependent: set(factor).
% 1.76/1.93
% 1.76/1.93 ------------> process usable:
% 1.76/1.93 ** KEPT (pick-wt=6): 1 [] -subset(A,empty_set)|A=empty_set.
% 1.76/1.93 ** KEPT (pick-wt=11): 2 [] -subset(A,B)| -subset(A,C)|subset(A,intersection(B,C)).
% 1.76/1.93 ** KEPT (pick-wt=3): 3 [] -member(A,empty_set).
% 1.76/1.93 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.76/1.93 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.76/1.93 ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.76/1.93 ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.76/1.93 ** KEPT (pick-wt=8): 8 [] subset(A,B)| -member($f1(A,B),B).
% 1.76/1.93 ** KEPT (pick-wt=6): 9 [] A!=B|subset(A,B).
% 1.76/1.93 ** KEPT (pick-wt=6): 10 [] A!=B|subset(B,A).
% 1.76/1.93 ** KEPT (pick-wt=9): 11 [] A=B| -subset(A,B)| -subset(B,A).
% 1.76/1.93 ** KEPT (pick-wt=5): 12 [] -empty(A)| -member(B,A).
% 1.76/1.93 ** KEPT (pick-wt=9): 13 [] A!=B| -member(C,A)|member(C,B).
% 1.76/1.93 ** KEPT (pick-wt=9): 14 [] A!=B|member(C,A)| -member(C,B).
% 1.76/1.93 ** KEPT (pick-wt=13): 15 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 1.76/1.93 ** KEPT (pick-wt=3): 17 [copy,16,flip.1] empty_set!=$c3.
% 1.76/1.93
% 1.76/1.93 ------------> process sos:
% 1.76/1.93 ** KEPT (pick-wt=3): 22 [] A=A.
% 1.76/1.93 ** KEPT (pick-wt=8): 23 [] subset(A,B)|member($f1(A,B),A).
% 1.76/1.93 ** KEPT (pick-wt=7): 24 [] intersection(A,B)=intersection(B,A).
% 1.76/1.93 ** KEPT (pick-wt=3): 25 [] subset(A,A).
% 1.76/1.93 ** KEPT (pick-wt=6): 26 [] empty(A)|member($f2(A),A).
% 1.76/1.93 ** KEPT (pick-wt=13): 27 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 1.76/1.93 ** KEPT (pick-wt=3): 28 [] subset($c3,$c2).
% 1.76/1.93 ** KEPT (pick-wt=3): 29 [] subset($c3,$c1).
% 1.76/1.93 ** KEPT (pick-wt=5): 30 [] intersection($c2,$c1)=empty_set.
% 1.76/1.93 ---> New Demodulator: 31 [new_demod,30] intersection($c2,$c1)=empty_set.
% 1.76/1.93 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 1.76/1.93 22 back subsumes 21.
% 1.76/1.93 22 back subsumes 20.
% 1.76/1.93 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] intersection(A,B)=intersection(B,A).
% 1.76/1.93 >>>> Starting back demodulation with 31.
% 1.76/1.93
% 1.76/1.93 ======= end of input processing =======
% 1.76/1.93
% 1.76/1.93 =========== start of search ===========
% 1.76/1.93
% 1.76/1.93 -------- PROOF --------
% 1.76/1.93
% 1.76/1.93 ----> UNIT CONFLICT at 0.00 sec ----> 61 [binary,59.1,17.1] $F.
% 1.76/1.93
% 1.76/1.93 Length of proof is 3. Level of proof is 2.
% 1.76/1.93
% 1.76/1.93 ---------------- PROOF ----------------
% 1.76/1.93 % SZS status Theorem
% 1.76/1.93 % SZS output start Refutation
% See solution above
% 1.76/1.93 ------------ end of proof -------------
% 1.76/1.93
% 1.76/1.93
% 1.76/1.93 Search stopped by max_proofs option.
% 1.76/1.93
% 1.76/1.93
% 1.76/1.93 Search stopped by max_proofs option.
% 1.76/1.93
% 1.76/1.93 ============ end of search ============
% 1.76/1.93
% 1.76/1.93 -------------- statistics -------------
% 1.76/1.93 clauses given 5
% 1.76/1.93 clauses generated 55
% 1.76/1.93 clauses kept 57
% 1.76/1.93 clauses forward subsumed 25
% 1.76/1.93 clauses back subsumed 3
% 1.76/1.93 Kbytes malloced 976
% 1.76/1.93
% 1.76/1.93 ----------- times (seconds) -----------
% 1.76/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.76/1.93
% 1.76/1.93 That finishes the proof of the theorem.
% 1.76/1.93
% 1.76/1.93 Process 4623 finished Wed Jul 27 10:46:50 2022
% 1.76/1.93 Otter interrupted
% 1.76/1.93 PROOF FOUND
%------------------------------------------------------------------------------